PHGN341: Thermal Physics
Final Exam
May 4, 2004
NAME:
1. [20] A 2000 Megawatt nuclear-powered electricity generating plant operates on a Rankine cycle steam engine between
(T1 = 20 C,P1 = .023 bar) and (T3 = 500 C, P3 = 300 bar). The attached tables contain useful thermodynamic data.
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(a) What is the minimum mass of water that must pass through the generating
plant turbines per second?
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Pressure
(Steam)
(Water)
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(Water + Steam)
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Volume
(b) The waste heat is dumped into a nearby river which has a flow rate of 104 kg per second. Upstream from the plant
the temperature of the river water is 20 C. What is the temperature of the river water downstream from the plant?
2. A hydrogen fuel cell operates by combining oxygen gas and hydrogen gas to form water (liquid) at standard pressure
and temperature. The process involves the transfer of two electrons per molecule of water formed. The attached table
contains the thermodynamic properties of the materials involved in the hydrogen fuel cell process.
a. What is the voltage of a hydrogen fuel cell?
b. What is the change in the entropy the fuel constituents (hydrogen and oxygen) per mole of water produced?
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c. How much heat is delivered to the environment per mole of water produced?
3. Aluminum silicate (Al2 SiO5 ) can exist in three crystalline forms: kyanite, andalusite, and sillimanite. The thermodynamic properties of these forms are given in the table below. The temperature of the earth increases by about 20 K
per kilometer depth while the pressure increases by about 3×104 Pa per kilometer depth.
Substance
kyanite
andalusite
sillimanite
∆f H (kJ)
-2594.29
-2590.27
-2587.76
∆f G (kJ)
-2443.88
-2442.66
-2440.99
S (J/K)
83.81
93.22
96.11
V (cm3 )
44.09
51.53
49.90
What is the stable form of aluminum silicate at a depth of 100 km?
4. Consider a single sodium atom in the sun’s atmosphere. Calculate the grand partition function for a single sodium
atom by treating the sodium atom as a two state system, one neutral and one ionized. Approximate the chemical
potential of the free electrons in the sun’s atmosphere as an ideal gas. What is the probability that a sodium atom in
the sun’s atmosphere is ionized? (DATA: The binding energy of the electron to sodium is 5.15 eV; the electron density
in the solar atmosphere is 2 × 1013 e/cm3 ; the temperature of the sun’s atmosphere is 5,780 K.)
5. [15] Consider a system consisting of three spin-2 atoms. Each atom can have five possible values for its z-component of
angular momentum: m = +2, +1, 0, −1, −2.
(a) How may microstates are there?
(b) Assuming all microstates are accessible, what is the probability the system is in the macrostate of mtotal = 0?
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6. [20] In this problem you will treat the atomic nucleus as a fermi gas. First some basic nuclear terminology and
phenomenology. The nucleus is composed of neutrons and protons. Let N equal the number of neutrons, Z equal the
number of protons, and A be the total number of nucleons (protons and neutrons), A = N + Z. Nucleons bind together
with very short range forces which means they pack together like spheres. Thus, the nucleon density is a constant and
volume scales like the nucleon number, A, and therefore the nuclear radius scales like the cube root of the volume, or
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R = r0 A 3 . A fit to nuclear data gives r0 = 1.2 fm which is constant for all nuclei. The proton and neutron each have
about the same mass (939 MeV/c2 ) and are spin-1/2 fermions. In this problem we will treat the lead nucleus (A = 208,
Z = 82, and N = 120). Assume the lead nucleus is spherical and treat it as a fermi gas of protons and neutrons.
(a) Find the neutron density for lead (number of neutrons per cubic femtometer).
(b) What is the fermi momentum (in MeV/c) for the neutrons in lead?
(c) What is the average kinetic energy (in MeV) of a neutron in lead?
(d) Scale your neutron value to find the average kinetic energy of a proton in lead.
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